RouterInterp: Understanding Superposed Specialisation in Mixture of Experts Routing

AI summary

Overview

• Research area: Mechanistic interpretability of Sparse Mixture-of-Experts (MoE) language models, combining sparse autoencoders (SAEs) with automated natural-language explanation pipelines.
• Technical level: Intermediate — the paper assumes familiarity with transformer FFN layers, top-k routing, and SAE basics, though its central argument (experts are polysemantic) is stated plainly.
• Scope: The paper proposes and tests the Superposed Specialisation Hypothesis for MoE experts on two models (OLMoE-1B-7B and gpt-oss-20b), then introduces RouterInterp, an SAE-based method for generating explanations of expert routing.

What This Paper Is About

MoE models route each token to only a few experts, and the standard assumption has been that each expert specialises in one coherent domain (e.g. medical text or mathematics). Prior interpretability work built on that assumption has largely failed to recover clean, interpretable expert roles. This paper argues the assumption is wrong: experts specialise in disjoint collections of fine-grained features spanning unrelated micro-domains, and it builds a method that explains routing on that basis.

Key Contributions

1. The Superposed Specialisation Hypothesis (SSH): a formal alternative to the Domain Specialisation Hypothesis (DSH), stating that experts specialise in disjoint, semantically heterogeneous collections of features rather than a single coherent domain, supported by two theoretical arguments (interference minimisation and load balancing).
2. Empirical evidence for the SSH: for each expert, the top-n predictive SAE latents are spread across many distinct semantic clusters (mean G = 11.3 on gpt-oss-20b layer 20 and 10.8 on OLMoE-1B-7B layer 15, out of an upper bound of n = 20), far from the G = 1 the DSH predicts.
3. RouterInterp: an SAE-based method that identifies the latents most predictive of each expert's routing, collects positive/negative activating contexts per feature, and generates a unified natural-language explanation of the expert.
4. Evaluation and baselines: a scoring setup adapted from AutoInterp Detection, plus ablations showing the gain comes from SAE feature decomposition rather than from the LLM explainer; RouterInterp reaches a mean explanation score of 0.49 on gpt-oss-20b and 0.60 on OLMoE-1B-7B.

Main Findings

• Routing is polysemantic, not monosemantic: For each expert, the top n = 20 predictive SAE latents are clustered semantically from their generated natural-language explanations (embedded with all-MiniLM-L6-v2, clustered by k-means, silhouette selects K ≈ 50). Mean number of clusters G is 11.3 for gpt-oss-20b (layer 20) and 10.8 for OLMoE-1B-7B (layer 15), versus the DSH prediction of G = 1 and a random-assignment value of about 16.6 clusters.
• Some residual thematic coherence remains: The observed G values sit below random cluster assignment, suggesting experts' predictive latents are more related than arbitrary collections while still spanning many disjoint micro-domains.
• RouterInterp beats token-statistics baselines everywhere: Mean F1 of 0.492 (s = 128) on gpt-oss-20b and 0.602 on OLMoE-1B-7B, versus 0.299 and 0.342 for Unigram Lookup and 0.383 and 0.305 for Expert Impact AutoInterp. That is roughly 65% (gpt-oss-20b) and roughly 76% (OLMoE-1B-7B) mean F1 improvement over Unigram Lookup, and roughly 28% over Expert Impact AutoInterp on gpt-oss-20b.
• Large advantage over all baselines, at every depth: RouterInterp wins at every tested layer on both models (layers 4, 8, 12, 16, 20 of gpt-oss-20b; layers 3, 11, 15 of OLMoE-1B-7B).
• SAE decomposition is the key ingredient, not the LLM explainer: In the gpt-oss-20b ablations, verbalising token statistics with an LLM improves explanations only modestly (from 0.30 / 0.31 to 0.35 / 0.42 mean F1), and Expert Activations AutoInterp performs on par with Bigram AutoInterp (both 0.417 mean F1). RouterInterp gains +18% over the best of these LLM-based explainers.
• The two ablations fail in complementary ways: Bigram descriptions are narrow (precision 0.39, recall 0.59); full-window descriptions are broad (precision 0.30, recall 0.81). Grouping evidence by SAE feature improves precision and recall together (precision 0.47, recall 0.64; 0.495 mean F1 at s = 64).
• Robust to SAE sparsity: 0.495 for s = 64 versus 0.492 for s = 128 on gpt-oss-20b.
• SAE quality bounds explanation quality: OLMoE's SAEs are smaller and reconstruct better (32k latents, FVU 0.007–0.218 versus 131k latents for gpt-oss). Within gpt-oss-20b, layer 16 has the worst SAE reconstruction (FVU 0.19–0.23), the weakest routing prediction, and is the only layer where a matched-sparsity neuron probe outperforms the SAE basis.
• Expert Impact AutoInterp is volatile: On OLMoE-1B-7B it falls below Unigram Lookup (0.305 vs 0.342); for 19% of experts its descriptions are overly narrow and score exactly zero.
• Scores are not comparable to Herbst et al. (2026): They report F1 > 0.8 for most experts using a 10/10 positive–negative balance and a scorer prompt accepting rough hypothesis fit, whereas this paper uses a 15% positive rate and requires contextual match to a concrete activation pattern. A trivial always-predict-active classifier scores F1 0.67 at 10/10 balance versus 0.26 at the 15% positive rate.
• Expert descriptions are logical disjunctions: Automated interpretations frequently describe experts as activating on unrelated feature combinations, for example "C/C++ preprocessor directives" together with "spices and herbs", or "medical conditions" together with "electronic components".
• Apparent domain specialisation is participation, not exclusivity: Prior results on task pruning, multilingual experts, and safety-refusal toggling show an expert participates in a language, task, or behaviour — not that this is the only thing it does.

Methodology in Plain English

The authors first set up competing hypotheses about how experts behave. If there are more fine-grained categories in real data (which they call "micro-domains") than there are experts, then by the Pigeonhole Principle several categories must land in the same expert. The DSH says those are similar categories forming one coherent domain; the SSH says they are dissimilar categories forming a disjoint union of features, mirroring the superposition phenomenon seen in individual neurons.

To test this, they use SAEs, which decompose a model's activations into sparse, interpretable features (SAE latents). These latents act as stand-ins for micro-domains. For each expert they take the latents that best predict its activation, generate natural-language explanations of each latent from its most activating examples, embed those explanations, and cluster them. The number of distinct clusters an expert's latents occupy (G) directly distinguishes the hypotheses: 1 for the DSH, up to n for the SSH.

RouterInterp then turns the SSH into a practical explanation tool in three stages. First, it identifies the SAE features most relevant to each expert by approximating the effect of ablating each feature on whether that expert is selected, keeping the top-45 per expert with each feature assigned to at most one expert. Second, it collects context windows centred on tokens where each feature is active, split into positives (feature active and token routed to the expert) and negatives (feature active but token not routed there). Third, it prompts an LLM explainer with these feature-grouped, positive-versus-negative examples and asks for a single prose description of when the expert is selected.

Evaluation adapts AutoInterp Detection scoring: a separate LLM scorer reads the explanation and decides whether highlighted tokens in held-out windows match it, producing a binary prediction checked against ground-truth routing and reported as F1. Baselines are Unigram Lookup and Bigram Lookup (token co-occurrence statistics in the style of prior work), Unigram and Bigram AutoInterp (the same statistics summarised by an LLM), Expert Activations AutoInterp (full activating passages ranked by router score), and Expert Impact AutoInterp (passages ranked by expert impact on the residual stream, plus Logit Lens tokens).

Setup: OLMoE SAEs trained on OLMoE-mix-0924 with Top-K SAEs over 100M tokens at layers 3, 7, 11, and 15 (of 16), sparsity s = 32 and 32,768 features; gpt-oss-20b (24 layers) uses pretrained BatchTopK SAEs at layers 4, 8, 12, 16, and 20 with 131,072 features and s in {64, 128}. Routing analysis and scoring use the Pile. Explanation generation and scoring use the Delphi library, with Claude Sonnet 5 as explainer and GPT-5.6 Luna as scorer, over 15 positive and 85 negative examples per expert (15% positive rate, approximating k/E ≈ 12.5% for gpt-oss with k = 4, E = 32 and OLMoE with k = 8, E = 64). A small human evaluation found human–LLM agreement comparable to human–human agreement.

Why This Matters

Impact on research. The paper reframes a long-standing negative result — many interpretability efforts that assumed monosemantic experts could not explain routing — as evidence that the wrong assumption was being made. It also offers a success case for SAE-based methods in the middle of an ongoing debate about their usefulness, aligning with the view that SAEs are valuable for discovering unknowns rather than acting on already-known concepts.

Real-world applications:

• Debugging and auditing deployed MoE models: understanding why a token reaches a given expert helps diagnose unexpected behaviours in production systems.
• Safety analysis: prior work showed that ablating a small set of experts can toggle safety refusals; knowing that an expert has many unrelated roles warns against treating such experts as single-purpose safety components.
• MoE architecture design: the SSH explanation of why dissimilar micro-domains land in the same expert informs how routers, expert counts, and load-balancing losses could be designed for more interpretable behaviour.
• Model compression and pruning: task-specific expert pruning results make more sense when experts are understood as participating in, rather than owning, a task — which affects how aggressively experts can be removed.

Industry relevance. MoE models are a mainstream approach to scaling frontier language models efficiently, activating only 2–15% of parameters per input and typically using 8 to 128 experts per layer. The two models studied (OLMoE-1B-7B and gpt-oss-20b) are open and widely used, and the method scales across model depth, making it directly applicable to teams interpreting or maintaining MoE deployments.

Future Directions

1. Test the functional routing hypothesis: Do experts group tokens by input similarity (similar semantic features) or by functional similarity (similar downstream transformations needed)? The authors suggest functional similarity with experts performing computation in superposition is a promising framing.
2. Scale RouterInterp to frontier architectures: beyond the 1B–20B parameter range, including models with shared experts and different routing methods such as Expert Choice routing.
3. Improve explanation conciseness and exploration: explanations grow with the number of aggregated features, so compression methods and interactive formats such as feature dashboards on Neuronpedia are proposed as optimisations.
4. Interpret routing collections or paths rather than single experts: with few experts but combinatorially many top-k expert sets and cross-layer routing paths, these higher-level units may prove more tractable targets.
5. Improve SAE quality: since RouterInterp performance correlates with SAE reconstruction quality across layers (higher FVU means weaker routing prediction), better SAEs should directly improve explanations.

Target Audience

Mechanistic interpretability researchers and MoE practitioners benefit most: those studying expert routing, sparse autoencoders, or polysemanticity; engineers interpreting or debugging deployed MoE models such as OLMoE and gpt-oss; and safety researchers who need to know whether an expert's role can be described by a single concept. Readers wanting a conceptual introduction to why experts are not monosemantic will find Sections 1 and 3 accessible, while the methods and evaluation details in Section 4 assume familiarity with SAEs and routing.

Authors’ abstract

Sparse Mixture of Experts (MoE) models scale more efficiently than dense models by routing tokens to modular expert networks that are only active for processing a fraction of tokens. A leading hypothesis for the performance of MoE models is that each expert specialises in a single, coherent domain. However, interpretability efforts that assume this hypothesis have generally been unsuccessful. We propose and present evidence for an alternative account that we call the Superposed Specialisation Hypothesis (SSH): experts specialise in a disjoint union of fine-grained features rather than one broad domain. Leveraging the SSH, we introduce RouterInterp, a method for interpreting expert routing that identifies Sparse Autoencoder features most predictive of routing decisions and produces unified natural language explanations. On gpt-oss-20b, RouterInterp explains expert routing with ${\sim}65\%$ higher detection accuracy than prior token statistics based methods. This work provides a scalable method for generating more accurate explanations of expert routing and increases our understanding of a previously uninterpretable component of foundation models.